Magnetic Effect of Electric Current
Directions of Electric and Magnetic Fields Right Hand Thumb Rule: Fleming's Left Hand Rule : Motion : Thumb ; Magnetic Field : First Finger ; Current : Middle Finger Fleming's Right Hand Rule : Motion : Magnetic Induction Biot Savart's Law B = (µ0/4π) (I dl sin θ)/(r2) Magnetic Induction 'straight conductor' B = (µ0I)/(2πa) 'Circular Conductor' B = (µ0I)/(2a) 'At a distance from circular conductor' B = µ0I a2 / (a2+x2)3/2 Force between two parallel conductors B = (µ0I1I2)/(2πa) Lorentz Force 'Electric Force' Fq = qE Force experienced by a charge = qvBsinθ 'Magnetic Force' Fm = Q (vxB) 'Electromagnetic Force' Fem = qE + q(vxB) Force experienced by a conductor in magnetic field = IBlsinθ Torque Torque = MB sinθ Additional Configurations # Field due to two concentric coils of radii r1 and r2 having turns N1 and N2 in which same current I is flowing in anticlockwise direction at their common center O :- B = µ0 I/2 N2/r2 ( + if current is in same direction and - if opposite directions . ) 2. Field due to semicircular arc of wire at the center O of the arc:- * B = (µ0 πI) / (4π''R'') 3. Field due to straight wire and loop at the center O of the loop (If the current in the looop in anticlockwise direction):- B = (µ0 /4π) 2I/R 4. Field due to semicircular concentric arcs of wire : B = µ0I/4 1/''a''-1/''b'' 5. Field due to 2 semicircles of radius R & r : B = µ0I/4 1/R+1/r Ampere's Circuital Law Ampere's Circuital Law states that the line integral of Magnetic Induction is equal to the product of absolute permeability and Current flowing through the coil . Magnetic Lines of Force are also referred to Amperian Loops . ∫ B.dl = μ0 I Straight Conductor B = μ0 I / 2πa Solenoid B = μ0 NI Torroid B = μ0 NI Galvanometer A Galvanometer is used to measure a small current . Thus, a Galvanometer is mostly used to only detect the presence of current . To measure larger values of current , a galvanometer is converted to an Ammeter by connecting a Shunt resistance of low resistance in parallel to the galvanometer . A Voltmeter can be prepared from a galvanometer by adding a resistor of infinitely high resistance in series to the galvanometer . Moving Coil Galvanometer A moving Coil Galvanometer consists of a soft iron core of high permeability , on which a rectangular coil is wound . The coil is then placed between the poles of a strong magnet . The coil rotates with a change in Current ... i α θ Suspended The coil is suspended from a rigid support . On the suspension cable , there is a mirror . Light is made to fall on the mirror . When the deflection begins , the reflected ray moves along a calibrated scale . This measures the current . Pivoted The coil is pivoted from both ends . The top end of the coil is connected to a pointer , which moves with deflection in the coil . The pointer is then pointed on a semi-circular scale . The pivoted set-up is easier to handle than the suspended set-up . Ammeter To measure larger values of current , a galvanometer is converted to an Ammeter by connecting a Shunt resistance of low resistance in parallel to the galvanometer . The maximum current measured by galvanometer is called as Galvanometer Current (ig) or Full scale deflection . When shunt is connected , only a fraction of current flows through the galvanometer . For e.g. consider a Galvanometer of Full Scale Deflection 10 mA . Suppose the range of Ammeter is increased to 100 mA . Now if 50 mA Current is flowing through the Ammeter , 5 mA will flow through Galvanometer and 95 mA will flow through Shunt . Thus , the galvanometer reading will be 5 . But , since 10 mA was increased to 100 mA (10 times ) the least count also changes . Now , the least count is 10 mA as opposed to 1 mA initially . Thus the reading is 5 and the value of Current measured is 50 mA . The shunt resistance should be of lower resistance , so that most current flows through the shunt . The Shunt resistance should be decreased to increase the range of an Ammeter . Voltmeter A Voltmeter can be prepared from a galvanometer by adding a resistor of infinitely high resistance in series to the galvanometer . The added resistance provides a huge potential drop , which is required to measure the potential difference . To increase the range of voltmeter , the resistance should be increased . Cyclotron Cyclotron is an instrument used to accelerate a positively charged particle . The cyclotron consists of two hollow semi-cylindrical metal boxes . These are called as 'dees' . There s a gap between the dees . The dees are kept under a strong magnetic field . A potential of the order 106 V is applied between the dees and high frequency of 107 Hz . The particle is kept in the gap . Due to high frequency of Alternating voltage , the dees keep switchng their polarities . If D1 is at negative potential at first , the charged particle moves away from D2 . This force acting on the charge due to magnetic field provides necessary centripetal force . This force helps the charge to be accelerated and moves towards the gap between the dees . r = mv/ qB t = 2mπ / qB = 2πr / v f = 1/t = qB / 2πm vmax = qBR / m 'K.E. = q2B2R2 / 2m ' Tangent Galvanometer B = BHtanθ μ0ni / 2r = BHtanθ Category:Physics